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Help! Thrid second and first order differential equation

  1. Jul 6, 2012 #1
    Help! Thrid second and first order differential equation!!!!

    I have no idea how to accomplish this problem. If anyone knows help please help me solve this example before I take my test!

    Solve
    y''' - y'' - y' + y - x = 0
     
  2. jcsd
  3. Jul 6, 2012 #2

    HallsofIvy

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    Re: Help! Thrid second and first order differential equation!!!!

    Have you never taken a course in differential equations? If not I wonder why you would be trying to solve an equation like this. If you have, this should be relatively easy. It is a "linear equation with constant coefficients". The associated homogeneous equation is y'''- y''- y'+ y= 0 which has characteristic equation [itex]r^3- r^2- r+ 1= 0[/itex]. An obvious solution to that is r= 1 and then you can divide by r- 1 to get a quadratic equation to solve for the other two roots.

    To find a specific solution to the entire equation, try y(x)= Ax+ B for some numbers A and B.
     
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